We present a simple method for analytic continuation of harmonic sums near negative and positive integer numbers. We provide a precomputed database for the exact expansion of harmonic sums over a small parameter near these integer numbers, along with MATHEMATICA code, which shows the application of the database for actual problems. We also provide the FORM code that was used to obtain the database mentioned above. The applications of the obtained database for the study of evolution equations in the quantum field theory are discussed.

中文翻译：

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整数值附近谐波和的解析延拓

我们提出了一种简单的方法来分析在负整数和正整数附近的调和和的延拓。我们提供了一个预先计算的数据库，用于在这些整数附近的一个小参数上精确扩展谐波和，以及 MATHEMATICA 代码，它显示了数据库在实际问题中的应用。我们还提供了用于获取上述数据库的 FORM 代码。讨论了所得数据库在量子场论演化方程研究中的应用。